Moment of inertia measuring instrument

ABSTRACT

An inverted torsion pendulum which may be used to measure the moment of inertia of physical parts of any size or shape. In one preferred embodiment, a taut wire is placed in tension in a rigid fixed frame. A test object is attached to an object mounting surface located above the fixed frame and concentric with the longitudinal axis of the taut wire. A rigid support structure couples this object mounting surface to the center of the taut wire. Bearings limit the motion of the oscillating assembly to pure rotation. The period of oscillation of the torsion pendulum is determined with a magnetic reed switch and electronic period counter and the moment of inertia of the test object calculated using conventional methods.

United States Patent Boynton 51 Sept. 26, 1972 MOMENT OF INERTIAMEASURING INSTRUMENT [72] inventor: Richard Studley Boynton, 81Hillcrest Terrace, Meriden, Conn. 06450 22 Filed: Feb. 2,1971

21 Appl.No.:lll,979

[52] 0.8. CI. ..73/65 [5|] Int. Cl. ..G0lm 1/10 [58] Field of Search..73/65, 99, 383

[56] References Cited UNITED STATES PATENTS 3,106,091 10/1963 Korr..73/65 3,473,370 10/1969 Mariniak ..73/65 Primary Examiner-Richard C.Queisser Assistant Examiner-Herbert Goldstein [57] ABSTRACT An invertedtorsion pendulum which may be used to measure the moment of inertia ofphysical parts of any size or shape. In one preferred embodiment, a tautwire is placed in tension in a rigid fixed frame. A test object isattached to an object mounting surface located above the fixed frame andconcentric with the longitudinal axis of the taut wire. A rigid supportstructure couples this object mounting surface to the center of the tautwire. Bearings limit the motion of the oscillating assembly to purerotation. The period of oscillation of the torsion pendulum isdetermined with a magnetic reed switch and electronic period counter andthe moment of inertia of the test object calculated using conventionalmethods.

5 Claims, 2 Drawing Figures DIGITAL PERIOD COUNTER PATENTED m2 3.693.413

SHEEI 1 0F 2 DIGITAL PERIOD C OUNTEH I N VENTOR. RICHARD STuDLEY BOYNTONMOMENT F INERTIA MEASURING INSTRUMENT This invention generally relatesto systems for measuring moment of inertia and more specifically to aninverted torsion pendulum for determining moment of inertia of objectsconveniently and accurately.

The proper design of any rotating device requires a knowledge of themoment of inertia of its parts. The moment of inertia of any rotatingobject is related to the torque required to accelerate the object, tothe stress on the driving member during acceleration, to the naturalresonant frequency of an object in the torsional mode, and inclosed-loop systems to the stability margin of the system. The moment ofinertia of objects composed of simple shapes may be calculated by wellknown methods. However, such calculations are time consuming compared todirect measurement. It is impractical to calculate the moment of inertiaof complex shapes or objects made of materials of varying density.Direct measurement of moment of inertia is also desirable in determiningvariations in production parts where moment of inertia is a criticalfactor.

The use of a torsion pendulum to measure moment of inertia is wellknown. However, the classical version of this pendulum was not practicalto use nor did it give accurate results. This invention offers apractical and accurate means of implementing the classical concept. Theclassical torsional pendulum consisted of a wire or thin rod mountedfrom some type of structure; the test object was hung from the end ofthis rod. The system had a number of practical disadvantages. First ofall, there was the difficulty of hanging the test object up side downfrom a thin rod. Secondly, there was the expense and space required forthe structure which supported the upper end of the rod. Thirdly, thetest object would not simply oscillate in a torsional sense-since theobject hung freely from a long thin rod, it was also free to oscillateback and forth in any direction, and to bounce up and down. Theseadditional motions made it extremely difficult to measure therotational.period of oscillation and produced errors. And finally, theweight of the test object would stretch the thin rod, changing itstorsional spring constant.

Recently, torsion pendulums have been designed using gas bearings. Thesesystems permit the torsion pendulum to be inverted and are veryaccurate. However, they are relatively expensive and require a source ofpressurized nitrogen or clean, dry air.

It is an object of the present invention to provide a torsion pendulumwhich is inverted but which does not require the use of a gas bearing.Another object of this invention is to restrict the motions of thetorsion pendulum other than pure rotation.

Another object of the invention is to provide a torsion pendulum towhich standard rotating machine parts such as shafts, gears, and pulleysmay be quickly and conveniently mounted.

In one embodiment of the invention, the test object to be measured isrigidly mounted on the object mounting surface on the top of the torsionpendulum; preferably the test object is mounted so that the rotationaxis of the instrument passes through the center of gravity of the testobject. The torsion pendulum is then twisted slightly and released sothat it oscillates about its axis. The period of oscillation of thetotal moving system is determined by the use of magnetic reed switchwhich produces electrical timing pulses at a particular angular positionof the oscillating system. These electrical timing pulses start and stopan electronic period counter or other accurate timing device. The momentof inertia of the total oscillating system may be calculated by squaringthis time period and multiplying it by a calibration constant. Thismeasured moment of inertia is the total of the test object and theinstrument itself. The moment of inertia of the instrument andassociated mounting hardware is now determined by removing the testobject, obtaining a new time period and repeating the basic calculation:

This tare" moment of inertia is then subtracted from the total measuredmoment of inertia to yield the moment of inertia of the test object.

The value of the calibration constant, C is then measured by mounting acalibration weight of precisely known moment of inertia on theinstrument, measuring the time period of oscillation and solving thefollowing equation for C.

where 1,. moment of inertia of calibration weight T time period withcalibration weight mounted T time period with calibration weight removedThe above procedure for measuring moment of inertia using a torsionpendulum is well known.

The invention will be better understood from the following exampleswhich are intended to serve as illustrations but in no way limit thescope of the claims. Reference will be made to the drawings where FIG. 1illustrates a first embodiment, and shows a test object mounted on theinstrument, and

FIG. 2 shows a second embodiment of the torsion pendulum.

DETAILS OF THE FIRST EMBODIMENT Referring to FIG. 1 showing the firstembodiment, a test object whose moment of inertia is to be determined(18) is attached to the object mounting surface (1) by means of a testfixture (19) whose inside diameter matches the outside diameter of theshaft on the test object. Test fixtures of various sizes and shapes maybe used to attach other size test objects to the object mountingsurface, so that any shape or size test object may be tested providedits weight is within the rating of the instrument. The object mountingsurface (1) is rigidly fastened to the rigid support structure (2) asare the wire clamps (6) and (20). During the operation of the torsionpendulum these objects remain in a fixed position relative to eachother, but as will be described later, this torsion assembly consistingof the items 1, 2, 6, and 20, oscillates relative to the other parts ofthe instrument. The torsion assembly is fastened to a torsionallyresilient member (in this Embodiment A, a taut wire) (3) by means of theclamps (6) and (20). No other part of the torsion assembly comes incontact with the fixed parts of the instrument. The taut wire (3) issupported on one end by clamp (4) which in turn is rigidly fastened tothe top plate (12) which is connected to the vertical supports (10) and(l l) which are fastened to the base (9). The other end of the taut wire(3) is fastened to clamp (5) which is attached to base (9) through atension adjusting screw (13). A starting lever (17) is moved in such adirection as to twist the taut wire (3) a small angle such as 5 and issharply released. This causes the torsion assembly to oscillate in arotational sense about the longitudinal axis of the taut wire (3). Thetorsion assembly will continue to oscillate back and forth at adecreasing amplitude as determined by the internal losses in the tautwire (3) and by other losses such as windage. A magnet (14) mounted onthe torsion assembly oscillates back and forth relative to a magneticreed switch (15) which is attached to the base (9) through the circuitboard (16). As the magnet (14) moves relative to the magnetic reedswitch (15), the magnetic reed switch (15) will open and close in amanner well known to those familiar with magnetic reed switches. Theoutput of the magnetic reed switch (15) is electrically connected to thecircuit board (16) which converts the closing of the switch to anelectrical signal which lasts for a relatively short period of time(such as 10 microseconds). This narrow timing pulse is introduced to theinput of an electronic period counter (21) or other accurate timingdevice. The first timing pulse starts the counter operating and thesecond timing pulse stops the counter at exactly one period ofoscillation later. The counter therefore reads the mechanical periodoscillation of the torsion pendulum. Other methods of measuring timeperiod may be used such as one employing a mirror mounted on the torsionassembly, and a light source and photocell mounted on the fixed part ofthe instrument.

The moment of inertia of the test object may be determined by takingtime period readings with and without the test object as describedpreviously.

DETAILS OF A SECOND EMBODIMENT F IG. 2 illustrates a second embodimentof the invention (in which the test object and test fixture are notshown for the sake of simplicity). This embodiment differs from thatshown in FIG. 1 in the following ways: the second wire clamp has beendeleted and the stiffness of the torsion assembly with respect tomotions other than oscillation about the longitudinal axis of the tautwire (3) has been increased by the addition of two radially restrainingmembers (bearings) (7) and (8). These bearings are rigidly fastened tothe rigid support structure (2). The taut wire (3) passes through thecenter of these bearings.

OTHER EMBODIMENTS It should be apparent that the torsionally resilientmember which in the first preferred embodiment comprised a single tautwire could be achieved instead by two taut wires mounted on the sameaxis-one clamped at (5) and (20) and the other clamped at (4) and (6).Or any number of wires with the same or differing cross section could bearranged along the same axis with various fixed structures between themto create the torsionally resilient member without changing the basicfunction of the torsionally resilient member.

It is also obvious that the taut Wire need not be a round wire but canbe any cross sectional shape, solid or hollow, provided it is strongenough to support the weight of the test object without significantlychanging its torsional stiffness and providing its torsional stiffnessis within certain practical limitations determined by factors such asthe timing accuracy and the rigidity of the test objects. The term"torsionally resilient member" (Item A in Claim 1) is therefore definedto include all wire means which are flexible in the torsional sense andrelatively rigid in the axial direction.

Many other means may be used to decrease the compliance of theoscillating parts to modes other than rotation about the longitudinalaxis of the taut wire. For example, bearings may be located outside thespace between the wire clamps (4) and (5) at a position which isconcentric with the longitudinal axis of the taut wire (3), and sometype of rigid structure may be employed to couple these bearings to therigid support structure (2). 0r only one bearing may be used rather thantwo. Or some type of pivot or crossed web flexure may be used toaccomplish the same purpose as the bearings shown in FIG. 2. In fact anymechanical device which limits the motion of the torsion assembly in adirection perpendicular to the longitudinal axis of the taut wire morethan it limits rotational motion about the longitudinal axis may be usedfor this purpose, and no effort will be made to list all such devices.

While the structure of the fixed frame, the rigid support structure, theobject mounting surface, and many other parts of the invention have beendescribed and illustrated in detail, it should be apparent to thoseskilled in the art that certain modifications and variations thereof arepossible in light of the above teachings. it is therefore, understoodthat the present disclosure has been made only by way of example andthat numerous changes in the construction and the combination andarrangement of parts may be resorted to without departing from thespirit and the scope of the invention.

I claim as my invention:

1. A torsion pendulum comprising:

A. A torsionally resilient member B. A fixed frame including means forfixedly supporting both ends of A so that A is in tension but free totwist with respect to its torsion axis passing through both supportedends.

C. An object mounting surface normal to the torsion axis of A andlocated beyond one end of A.

D. An attaching means comprising a rigid member extending from C to Aand connected to both C and at least one point on A intermediate theends of A.

E. A radially restraining means for limiting the motion of C in adirection normal to the torsion axis of A, so that the motion of C isprimarily torsional oscillation about the torsion axis of A, saidradially restraining means connected to at least one point on D and atleast one point on the combination of A and B.

F. Means for turning C relative to the torsion axis of A and thenreleasing C causing C to oscillate torsionally relative to the torsionaxis of A.

G. Means of timing the period of said oscillation of 2. The combinationrecited in claim 1 containing in addition at least one more radiallyrestraining means attached to a point on the combination of A and B andattached to D at a point on the torsion axis differing from 3,693,413 6the location of E, all said restraining means to be con- 5. Thecombination recited in claim 4, where G comcemric with the ml'sion axisprises a magnet attached to D and a magnetic reed The in ciaim whereinsaid switch attached to B, the output of said reed switch radiallyrestraining members are axial bearings.

4. The combination recited in claim 3, where said ob- 5 convened to.elecmcal timing signal which starts and ject is temporarily fastened tothe object mounting sur- Stops conventional electron: penod counter'face of C, and where A is a round wire.

1. A torsion pendulum comprising: A. A torsionally resilient member B. Afixed frame including means for fixedly supporting both ends of A sothat A is in tension but free to twist with respect to its torsion axispassing through both supported ends. C. An object mounting surfacenormal to the torsion axis of A and located beyond one end of A. D. Anattaching means comprising a rigid member extending from C to A andconnected to both C and at least one point on A intermediate the ends ofA. E. A radially restraining means for limiting the motion of C in adirection normal to the torsion axis of A, so that the motion of C isprimarily torsional oscillation about the torsion axis of A, saidradially restraining means connected to at least one point on D and atleast one point on the combination of A and B. F. Means for turning Crelative to the torsion axis of A and then releasing C causing C tooscillate torsionally relative to the torsion axis of A. G. Means oftiming the period of said oscillation of C.
 2. The combination recitedin claim 1 containing in addition at least one more radially restrainingmeans attached to a point on the combination of A and B and attached toD at a point on the torsion axis differing from the location of E, allsaid restraining means to be concentric with the torsion axis of A. 3.The combination recited in claim 2, wherein said radially restrainingmembers are axial bearings.
 4. The combination recited in claim 3, wheresaid object is temporarily fastened to the object mounting surface of C,and where A is a round wire.
 5. The combination recited in claim 4,where G comprises a magnet attached to D and a magnetic reed switchattached to B, the output of said reed switch converted to an electricaltiming signal which starts and stops a conventional electronic periodcounter.